Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
480 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22561048 | C2 | semidirect |
| 3. #22558922 | C2 | semidirect |
| 4. #22558816 | C2 | semidirect |
| 5. #22558120 | C2 | semidirect |
| 6. #22558080 | C2 | semidirect |
| 7. C67×#2995 | C2 | semidirect |
| 204. #2995 | D67 | semidirect |
| 210. C67 | #9340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571224 | 2 |
| #22561048 | 2 |
| #22558922 | 2 |
| #22558816 | 2 |
| #22558120 | 2 |
| #22558080 | 2 |
| C67×#2995 | 2 |
| #9340 | 67 |